Question: Solve for $x$ and $y$ using elimination. ${x+5y = 56}$ ${-x+4y = 34}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $9y = 90$ $\dfrac{9y}{{9}} = \dfrac{90}{{9}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {x+5y = 56}\thinspace$ to find $x$ ${x + 5}{(10)}{= 56}$ $x+50 = 56$ $x+50{-50} = 56{-50}$ ${x = 6}$ You can also plug ${y = 10}$ into $\thinspace {-x+4y = 34}\thinspace$ and get the same answer for $x$ : ${-x + 4}{(10)}{= 34}$ ${x = 6}$